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Beurling Generalized Numbers Mathematical Surveys And Monographs Mathematical Surveys And Monographs 213 Harold G Diamond

SKU: BELL-51992382

$ 31.00 ~~$ 45.00~~ (-31%)

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Beurling Generalized Numbers Mathematical Surveys And Monographs Mathematical Surveys And Monographs 213 Harold G Diamond instant download after payment.

Publisher: American Mathematical Society

File Extension: PDF

File size: 2.16 MB

Pages: 244

Author: Harold G. Diamond, Wen-Bin Zhang

ISBN: 9781470430450, 1470430452

Language: English

Year: 2016

Product desciption

Beurling Generalized Numbers Mathematical Surveys And Monographs Mathematical Surveys And Monographs 213 Harold G Diamond by Harold G. Diamond, Wen-bin Zhang 9781470430450, 1470430452 instant download after payment.

Generalized numbers" is a multiplicative structure introduced by A. Beurling to study how independent prime number theory is from the additivity of the natural numbers. The results and techniques of this theory apply to other systems having the character of prime numbers and integers; for example, it is used in the study of the prime number theorem (PNT) for ideals of algebraic number fields. Using both analytic and elementary methods, this book presents many old and new theorems, including several of the authors' results, and many examples of extremal behavior of g-number systems. Also, the authors give detailed accounts of the $L^2$ PNT theorem of J. P. Kahane and of the example created with H. L. Montgomery, showing that additive structure is needed for proving the Riemann hypothesis. Other interesting topics discussed are propositions "equivalent" to the PNT, the role of multiplicative convolution and Chebyshev's prime number formula for g-numbers, and how Beurling theory provides an interpretation of the smooth number formulas of Dickman and de Bruijn.